At the end of the day modern conservatism around the world is not defined by attachment to some particular organ of government. Whilst most conservative parties differ on details due to differing national circumstances, most of them come down to common positions in terms of economics & taxation, the rule of law and a strong position on the world stage. There's no monarchy in that lot. Conservative politicians have committed acts of republicanism in the past, most notably when Stanley Baldwin forced Edward VIII's abdication (any choice or rejection of a head of state is republicanism) and I have no doubt that if this country does ever have a referendum on the subject we will see some Conservative party members at the forefront of a republic campaign. Malcolm Turnbull is no heretic in the international conservative family.